How to get product category ID based on post?

One option would be to use get_the_terms() to get the terms of the current post for certain taxonomy. Then loop the found terms and check, if one of them has certain ID.

$terms = get_the_terms( get_the_ID(), 'product_cat' );
if ( ! is_wp_error( $terms ) && $terms ) {
    foreach ($terms as $term) {
        if ( 123 === $term->term_id ) {
            echo '<img src="my-image.jpg">';
        }
    }
}

Another option could be to use has_term() to check, if the current post has certain term in a more compact way.

if ( has_term( $term_or_slug_or_term_id, 'product_cat' ) ) {
    echo '<img src="my-image.jpg">';
}